You don't need all those x's and (x)'s.   They just get in
the way. And we know they're understood.

Use conditional proof or indirect proof as needed:

1. R ⊃ (T • ∼E)	 
2. (Q • R) ⊃ E	   / R ⊃ ∼Q

3.             | R        Assumption for Conditional proof
4.             | T • ∼E   1,3, Modus Ponens
5.             |~E • T    4, Commutation
6.             |~E        5, Simplification
7.             |~(Q • R)  2,6,  Modus tollens
8.             |~Q ∨ ~R   7, DeMordan's law
9.             |~R ∨ ~Q   8, Commutation
10.            |~~R       3, Double negation
11.            |~Q        9,10, Disjunctive syllogism
12. R ⊃ ∼Q    lines 3-11  Conditional proof

Edwin